Optimization method for the inverse problem of reconstructing the source term in a parabolic equation
type: Item
instance of: scholarly article
title: Optimization method for the inverse problem of reconstructing the source term in a parabolic equation
zbMATH Open document ID: 1183.65118
author: Liu Yang
author: Zui-Cha Deng
author: Jianning Yu
author: G. W. Luo
published in: Mathematics and Computers in Simulation
publication date: 2009-11-16T00:00:00Z
review text: The authors consider an inverse problem of reconstructing in the parabolic heat equation a heat source term which depends on the spatial variable using a final temperature measurement. The authors use an optimal control framework to discuss this problem. The existence and a necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer for the cost functional are proved. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are also presented.
reviewed by: Damian Słota
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35Q05
Mathematics Subject Classification ID: 80A23
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 5633807
zbMATH Keywords: inverse problem
zbMATH Keywords: source term
zbMATH Keywords: optimization method
zbMATH Keywords: numerical results
zbMATH Keywords: parabolic heat equation
zbMATH Keywords: optimal control
zbMATH Keywords: stability
zbMATH Keywords: Landweber iteration
MaRDI profile type: Publication
full work available at URL: j.matcom.2009.06.031
OpenAlex ID: W2060722947
cites work: Q3568481
cites work: Q3771806
cites work: Determination of an Unknown Heat Source from Overspecified Boundary Data
cites work: An inverse problem of finding a parameter in a semi-linear heat equation
cites work: An inverse problem of finding a source parameter in a semilinear parabolic equation
cites work: Determination of a control function in three-dimensional parabolic equations
cites work: An inverse problem of determining the implied volatility in option pricing
cites work: Optimization method for an evolutional type inverse heat conduction problem
cites work: Identifying the coefficient of first-order in parabolic equation from final measurement data
cites work: Identifying the radiative coefficient of heat conduction equations from discrete measurement data
cites work: Q4895893
cites work: Q5520962
cites work: Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: weak solution approach
cites work: Inverse problems for partial differential equations
cites work: Determination of a spacewise dependent heat source
cites work: Numerical identifications of parameters in parabolic systems
cites work: Q3997763
cites work: Q3857636
cites work: Q3965502
cites work: An inverse problem of identifying the coefficient of parabolic equation
cites work: Source term identification in 1-D IHCP
DOI: 10.1016/J.MATCOM.2009.06.031
description: scientific article; zbMATH DE number 5633807